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该论文研究中心化二次神经网络的谱可辨识性与学习曲线辨识问题，构造了谱摘要一致但损失曲线不同的输入分布，并在高斯输入下证明单条精确标量损失曲线可辨识初始预测器与教师谱。
该论文通过冻结选中子集并只更换训练学习器的受控实验，证明样本价值（以及 easy-first 与几何覆盖策略的 crossover budget）是相对于目标学习器定义的，而非数据的固有属性。
This paper derives a unified token- and layer-wise decomposition of how learning from one token changes another prediction, connecting data attribution, catastrophic forgetting, and plasticity loss as distinct regimes of the same evolving update-behavior interaction. It yields forward-computable approximations enabling data selection, interference controls, and diagnostics for future learnability across models and training regimes.
This paper examines why evolutionarily stable cooperative outcomes in multi-agent systems may not be reachable through decentralized reinforcement learning algorithms, demonstrating distinct properties between stability and learning accessibility.
This paper develops a statistical-mechanical framework for analyzing learning dynamics in deep neural networks by shifting from parameter space to function space, deriving exact error dynamics and fluctuation-induced effects.
This paper analyzes how input correlations influence memory learning in linear recurrent neural networks, revealing that positive correlations reshape learning dynamics and set thresholds for memory retention.
This paper introduces a mechanistic framework analyzing transformer learning dynamics, identifying gradient starvation as a barrier to deep semantic dependencies and validating chain-of-thought strategies for effective learning.
The paper empirically characterizes the learning geometry of hybrid quantum forecasting models, comparing them to classical baselines using Neural Tangent Kernel dynamics and other metrics, showing that similar generalization can emerge from different optimization trajectories.
This paper develops a sharp pseudospectral theory for block-triangular Jacobians in coupled gradient descent, proving Kreiss-constant bounds and establishing iteration complexity results. The work exposes non-asymptotic, instance-dependent transient amplification phenomena relevant to bilevel optimization, two-time-scale stochastic approximation, and GAN training.
This paper proposes the 'support-before-frequency' hypothesis for discrete diffusion models, suggesting that models first learn the support (admissible sequences) before refining frequencies within the support. Theoretical analysis of small-noise reverse kernels and experiments on masked language diffusion models support this claim.
This paper develops a local theory of gradient descent near bifurcations in dynamical models, showing that the state-space neural tangent kernel collapses to a rank-one operator that dominates learning dynamics, making optimization effectively low-dimensional and predictable from normal forms.